1. Find the area of sector whose arc length and radius are 10cm and 5 cm respectively. (25 sq.cm)
2. A horse is tied to a pole fixed at one corner of a 30m x 30m square field of grass by a 10m long rope. Find the area of the part of the field in which the horse can graze. What will be the area of the field in which the horse can graze, if the pole was fixed at the middle of the side? (78.5sq. m. and 157sq. m)
3. The dimensions of a cuboid in cm are 16 x 14 x 20. Find its total surface area. (1648 sq cm)
4. The cuboidal water tank has length 2m, breadth 1.6m and height 1.8m. Find the capacity of the tank in litres. (5760 litres)
5. A solid cube is cut into two cuboids exactly at the middle as shown in the figure. Find the ratio of the total surface area of the given cube and that of the cuboid.
6. The radius and height of the cylinder are in the ratio 3:7 and its volume is 1584 cu.cm. Find its radius. (6 cm)
7. The curved surface area of a cone is 4070 sq. cm. and its diameter is 70 cm. What is the slant height? (37 cm)
8. A cone of height 24 cm has a place base of surface area 154 sq. cm. Find its volume. (V = 1232 cu.cm)
9. The surface area of a sphere is 616 sq.cm. What is the volume? (1437.33 sq cm.)
10. A cylindrical hole of diameter 30 cm is bored through a cubical wooden block with side 1 meter. Find the volume of the object so formed. (9,29,350)
11. A test tube has a diameter 20 mm and height 15 cm. The lower portion is hemispherical and the upper portion is cylindrical. Find the capacity of the test tube. (46.05)
OMTEX CLASSES
“THE HOME OF SUCCESS”
1. An arc of a circle having measure 360 has length 176m. Find the circumference of the circle. (1760m)
2. Two arcs of the same circle have their lengths in the ratio 4:5. Find the ratio of the areas of the corresponding sectors. (4:5)
3. Using the Euler’s formula, find V, if E= 30, F=12. If the solid figure is a prism, then the base of the polygon has how many sides? (V = 20 & 10 sides)
4. The side of a cube is 60 cm. find the total surface area of the cube. (Ans. 21600 sq cm)
5. A fish tank is in the form of a cuboid, whose external measures are 80 cm x 40 cm x 30 cm. The base, side faces and back face are to be covered with coloured paper. Find the area of the paper needed. (8000 sq cm.)
6. A beam of 4m long, 50 cm wide and 20 cm deep is made of wood which weighs 25 kg per m3. Find the weight of the beam. (10 kg)
7. Keeping the height same, how many times the radius of the given cylinder should be made to get the cylinder of double volume of the given cylinder? (√2 times)
8. The base radii of two right circular cones of the same height are in the ratio 2:3. Find the ratio of their volumes. (4:9)
9. The volumes of two spheres are in the ratio 27:64. Find their radii, if the sum of their radii is 28 cm. (12 cm & 16 cm)
10. If the radius of the sphere is doubled, what will be the ratio of its surface area and volume as to that of the first sphere? (4:1 & 8:1)
11. A toy is a combination of a cylinder, a hemisphere and a cone, each with radius 10 cm. Height of the conical part is 10 cm and the total height is 60 cm. Find the total surface area of the toy. (2512+628+3582.74=3582.74)